RUN: SPAI001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SPAI005E.rwl.conv LOG FILE PROCESSED: SPAI005E.rwl.conv_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 495 1 Alcala de Selva WIDTH_EARLY PIMU - 495 2 Spain krummholz pine 1960 4023-40 1820 1977 - 495 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 15 495101 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- 16 495102 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 1.765 0.605 0.123 1.914 0.189 0.751 2 495012 1914 1977 64 1.783 0.456 0.350 3.254 0.174 0.573 3 495021 1882 1977 96 1.600 0.928 1.368 3.900 0.181 0.911 4 495022 1886 1977 92 1.668 0.967 1.739 4.895 0.147 0.912 5 495031 1917 1977 61 2.440 0.736 0.516 3.816 0.165 0.738 6 495032 1922 1977 56 2.969 0.968 0.877 2.883 0.154 0.822 7 495041 1889 1977 89 1.611 0.648 0.456 2.756 0.184 0.845 8 495042 1885 1977 93 1.563 0.735 1.317 4.881 0.206 0.783 9 495051 1868 1977 110 1.785 1.303 1.585 5.460 0.175 0.890 10 495052 1864 1977 114 1.313 1.018 1.910 6.230 0.190 0.891 11 495081 1884 1977 94 1.529 0.605 1.577 5.436 0.187 0.739 12 495082 1868 1977 110 1.924 0.915 1.103 3.292 0.208 0.880 13 495091 1836 1977 142 1.222 0.494 0.383 2.605 0.203 0.795 14 495092 1854 1977 124 1.192 0.445 0.617 2.489 0.186 0.793 15 495101 1918 1977 60 2.719 1.393 0.669 2.735 0.207 0.867 16 495102 1917 1977 61 2.396 1.053 0.074 2.273 0.235 0.822 17 495111 1881 1977 97 1.675 0.841 0.336 2.267 0.178 0.907 18 495112 1893 1977 85 1.687 0.777 1.650 7.372 0.137 0.800 19 495141 1831 1977 147 1.444 0.528 0.708 3.249 0.226 0.682 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.243 0.397 0.384 3.322 0.218 0.669 21 495151 1900 1977 78 2.610 1.342 1.884 5.470 0.147 0.894 22 495152 1897 1977 81 2.373 1.139 0.840 3.346 0.150 0.901 NUMBER OF SERIES READ IN: 22 FROM 1820 TO 1977 158 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.841 0.831 0.930 3.811 0.184 0.812 STANDARD DEVIATION 29 0.515 0.299 0.600 1.464 0.027 0.091 MEDIAN (50TH QUANTILE) 92 1.681 0.809 0.774 3.307 0.185 0.822 INTERQUARTILE RANGE 45 0.845 0.413 1.193 2.160 0.040 0.140 MINIMUM VALUE 56 1.192 0.397 0.074 1.914 0.137 0.573 LOWER HINGE (25TH QUANTILE) 65 1.529 0.605 0.384 2.735 0.165 0.751 UPPER HINGE (75TH QUANTILE) 110 2.373 1.018 1.577 4.895 0.206 0.891 MAXIMUM VALUE 158 2.969 1.393 1.910 7.372 0.235 0.912 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.606 0.214 0.014 -1.382 5.509 -0.284 0.939 MINIMUM CORRELATION: -0.284 SERIES 495032 AND 495081 56 YEARS MAXIMUM CORRELATION: 0.939 SERIES 495051 AND 495052 110 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.450 0.550 0.551 SDEV 0.248 0.175 0.237 SERR 0.101 0.038 0.022 EPS 0.884 0.952 0.962 NSS 9.3 16.0 20.6 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1820 1977 158 1.569 0.491 0.712 3.019 0.138 0.841 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.624 0.404 -0.097 64 94 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 1.45 1.01 1.15 2.60 196.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.94 0.14 0.00 0.86 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 92. 45. 56. 65. 110. 158. |----------- RAW DATA CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.836 0.768 0.725 0.710 0.678 0.645 0.624 0.614 0.596 0.586 PACF 0.836 0.229 0.136 0.154 0.037 0.015 0.045 0.063 0.020 0.048 95% C.L. 0.159 0.246 0.301 0.342 0.378 0.407 0.433 0.455 0.475 0.494 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 4 0.741 0.607 0.087 0.039 0.181 |================== DETRENDED DATA CURVE FITS AND STATISTICS ==================| |------------------------ RESULTS OF FIRST DETRENDING -------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 495011 3 0.00000000 0.00000000 -0.02462456 2.57799506 2 495012 3 0.00000000 0.00000000 -0.01518246 2.27608633 3 495021 1 3.20155811 0.03438049 0.00000000 0.68129563 4 495022 1 3.75948167 0.05916144 0.00000000 1.00014114 5 495031 3 0.00000000 0.00000000 -0.03289688 3.45963931 6 495032 1 3.50069118 0.04220142 0.00000000 1.65483057 7 495041 3 0.00000000 0.00000000 -0.01851651 2.44459152 8 495042 1 2.57676244 0.04168842 0.00000000 0.92606920 9 495051 1 4.92255259 0.03704689 0.00000000 0.61992377 10 495052 1 4.15549135 0.04913498 0.00000000 0.59196568 11 495081 1 2.03580093 0.06931224 0.00000000 1.22752225 12 495082 3 0.00000000 0.00000000 -0.01603287 2.81409669 13 495091 3 0.00000000 0.00000000 -0.00722174 1.73867846 14 495092 3 0.00000000 0.00000000 -0.00989712 1.81058621 15 495101 1 4.65942764 0.06530499 0.00000000 1.53872871 16 495102 1 2.16590476 0.03470984 0.00000000 1.46472061 17 495111 3 0.00000000 0.00000000 -0.02740019 3.01714563 18 495112 1 2.63626409 0.03784816 0.00000000 0.91548526 19 495141 3 0.00000000 0.00000000 -0.00599510 1.88751471 SERIES IDENT OPTION A B C D 20 495142 3 0.00000000 0.00000000 -0.00317064 1.49478757 21 495151 1 5.79861212 0.09606358 0.00000000 1.87286294 22 495152 3 0.00000000 0.00000000 -0.04309779 4.14034271 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 0.996 0.213 0.254 3.002 0.185 0.394 2 495012 1914 1977 64 0.999 0.198 0.075 2.880 0.172 0.327 3 495021 1882 1977 96 1.002 0.266 0.572 2.964 0.178 0.685 4 495022 1886 1977 92 1.001 0.229 0.681 2.889 0.143 0.709 5 495031 1917 1977 61 0.999 0.185 0.724 3.544 0.162 0.415 6 495032 1922 1977 56 1.000 0.149 0.434 2.651 0.152 0.124 7 495041 1889 1977 89 1.009 0.316 1.032 4.805 0.182 0.655 8 495042 1885 1977 93 0.999 0.239 0.431 2.371 0.203 0.419 9 495051 1868 1977 110 0.998 0.256 0.538 3.293 0.174 0.625 10 495052 1864 1977 114 0.995 0.221 0.138 3.309 0.187 0.405 11 495081 1884 1977 94 1.000 0.260 1.036 3.757 0.186 0.568 12 495082 1868 1977 110 0.996 0.344 0.531 2.608 0.205 0.730 13 495091 1836 1977 142 0.991 0.299 0.054 2.535 0.201 0.652 14 495092 1854 1977 124 1.003 0.221 0.456 2.621 0.185 0.422 15 495101 1918 1977 60 1.001 0.327 0.083 3.757 0.208 0.650 16 495102 1917 1977 61 1.000 0.394 -0.225 2.076 0.235 0.767 17 495111 1881 1977 97 1.019 0.282 1.221 5.575 0.177 0.567 18 495112 1893 1977 85 0.998 0.230 0.114 2.509 0.134 0.631 19 495141 1831 1977 147 0.996 0.306 0.587 2.910 0.225 0.582 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.998 0.294 0.334 3.417 0.216 0.601 21 495151 1900 1977 78 1.001 0.222 0.165 2.075 0.146 0.659 22 495152 1897 1977 81 1.027 0.303 3.085 14.941 0.150 0.632 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.001 0.261 0.560 3.659 0.182 0.555 STANDARD DEVIATION 29 0.008 0.058 0.668 2.652 0.027 0.157 MEDIAN (50TH QUANTILE) 92 1.000 0.258 0.445 2.937 0.184 0.613 INTERQUARTILE RANGE 45 0.003 0.081 0.542 0.936 0.041 0.236 MINIMUM VALUE 56 0.991 0.149 -0.224 2.075 0.134 0.124 LOWER HINGE (25TH QUANTILE) 65 0.998 0.221 0.138 2.608 0.162 0.419 UPPER HINGE (75TH QUANTILE) 110 1.001 0.303 0.681 3.544 0.203 0.655 MAXIMUM VALUE 158 1.027 0.394 3.085 14.941 0.235 0.767 |------------------------ RESULTS OF SECOND DETRENDING ------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 495011 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 495012 -67 42 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 495021 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 495022 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 495031 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 495032 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 495041 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 495042 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 495051 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 495052 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 495081 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 495082 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 495091 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 495092 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 495101 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 495102 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 495111 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 495112 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 495141 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 495142 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 495151 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 495152 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 0.998 0.194 0.348 2.887 0.186 0.240 2 495012 1914 1977 64 0.999 0.189 0.429 3.203 0.171 0.259 3 495021 1882 1977 96 0.996 0.238 0.277 2.601 0.177 0.617 4 495022 1886 1977 92 0.998 0.206 0.560 2.564 0.143 0.631 5 495031 1917 1977 61 0.997 0.162 0.762 3.922 0.162 0.256 6 495032 1922 1977 56 0.999 0.143 0.414 2.758 0.152 0.061 7 495041 1889 1977 89 0.991 0.221 0.179 3.262 0.181 0.450 8 495042 1885 1977 93 0.999 0.226 0.442 2.605 0.203 0.352 9 495051 1868 1977 110 0.995 0.207 0.437 3.704 0.174 0.448 10 495052 1864 1977 114 0.999 0.202 0.255 3.452 0.187 0.273 11 495081 1884 1977 94 0.997 0.214 0.863 3.794 0.186 0.413 12 495082 1868 1977 110 0.986 0.252 0.466 2.728 0.205 0.499 13 495091 1836 1977 142 0.993 0.233 -0.082 2.760 0.200 0.467 14 495092 1854 1977 124 0.998 0.199 0.406 2.904 0.185 0.286 15 495101 1918 1977 60 0.993 0.293 -0.164 2.874 0.205 0.593 16 495102 1917 1977 61 0.984 0.354 0.062 2.591 0.235 0.715 17 495111 1881 1977 97 0.998 0.230 0.045 3.454 0.176 0.459 18 495112 1893 1977 85 0.997 0.178 0.278 2.572 0.134 0.415 19 495141 1831 1977 147 0.998 0.255 0.571 3.169 0.225 0.363 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.997 0.222 -0.213 4.238 0.216 0.270 21 495151 1900 1977 78 0.996 0.194 0.138 2.491 0.146 0.544 22 495152 1897 1977 81 0.997 0.201 0.562 4.499 0.148 0.500 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.996 0.219 0.320 3.138 0.182 0.414 STANDARD DEVIATION 29 0.004 0.044 0.279 0.587 0.027 0.157 MEDIAN (50TH QUANTILE) 92 0.997 0.210 0.377 2.895 0.183 0.432 INTERQUARTILE RANGE 45 0.003 0.039 0.329 0.849 0.041 0.227 MINIMUM VALUE 56 0.984 0.143 -0.213 2.491 0.134 0.061 LOWER HINGE (25TH QUANTILE) 65 0.995 0.194 0.138 2.605 0.162 0.273 UPPER HINGE (75TH QUANTILE) 110 0.998 0.233 0.466 3.454 0.203 0.500 MAXIMUM VALUE 158 0.999 0.354 0.863 4.499 0.235 0.715 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.268 0.188 0.012 -0.215 2.845 -0.272 0.798 MINIMUM CORRELATION: -0.272 SERIES 495012 AND 495022 64 YEARS MAXIMUM CORRELATION: 0.798 SERIES 495101 AND 495102 60 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.422 0.198 0.275 SDEV 0.242 0.259 0.228 SERR 0.099 0.056 0.021 EPS 0.871 0.798 0.887 NSS 9.3 16.0 20.6 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1820 1977 158 0.985 0.147 0.061 2.779 0.127 0.385 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.196 0.105 0.059 33 125 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.62 1.00 1.13 1.75 5.11 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.14 0.00 0.86 1.00 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.383 0.184 0.088 0.022 0.011 -0.017 -0.035 -0.122 -0.080 -0.105 PACF 0.383 0.044 0.004 -0.022 0.006 -0.024 -0.025 -0.114 0.009 -0.064 95% C.L. 0.159 0.181 0.186 0.187 0.187 0.187 0.187 0.187 0.189 0.190 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.148 0.383 |======================= POOLED AUTOREGRESSION ANALYSIS =======================| POOLED AUTOCORRELATIONS: LAG T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.460 0.262 0.148 0.017 -0.026 -0.015 -0.118 -0.215 -0.206 -0.267 YULE-WALKER ESTIMATES OF AUTOREGRESSION: ORDER T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 1 0.460 2 0.431 0.064 3 0.430 0.061 0.008 4 0.431 0.066 0.044 -0.085 5 0.429 0.067 0.045 -0.076 -0.021 6 0.429 0.069 0.044 -0.077 -0.030 0.023 7 0.432 0.065 0.034 -0.071 -0.021 0.079 -0.131 8 0.412 0.077 0.031 -0.082 -0.016 0.089 -0.064 -0.154 9 0.405 0.074 0.035 -0.083 -0.020 0.090 -0.060 -0.135 -0.047 10 0.399 0.055 0.027 -0.071 -0.023 0.079 -0.056 -0.125 0.008 -0.135 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 1007.69 972.12 973.47 975.46 976.33 978.26 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 980.18 979.47 977.66 979.32 978.40 SELECTED AUTOREGRESSION ORDER: 1 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.460 R-SQUARED DUE TO POOLED AUTOREGRESSION: 21.16 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 126.84 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.460 0.212 0.097 0.045 0.021 0.009 0.004 0.002 0.001 0.0004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 495011 1 0.075 0.246 2 495012 1 0.078 0.274 3 495021 1 0.382 0.618 4 495022 1 0.408 0.636 5 495031 1 0.066 0.256 6 495032 1 0.022 0.062 7 495041 1 0.232 0.455 8 495042 1 0.132 0.363 9 495051 1 0.203 0.451 10 495052 1 0.077 0.277 11 495081 1 0.183 0.413 12 495082 1 0.254 0.499 13 495091 1 0.261 0.471 14 495092 1 0.124 0.287 15 495101 1 0.412 0.597 16 495102 1 0.518 0.715 17 495111 1 0.228 0.472 18 495112 1 0.202 0.447 19 495141 1 0.145 0.364 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 495142 1 0.106 0.272 21 495151 1 0.322 0.560 22 495152 1 0.274 0.517 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.214 0.421 STANDARD DEVIATION 0 0.132 0.157 MEDIAN 1 0.203 0.449 INTERQUARTILE RANGE 0 0.168 0.240 MINIMUM VALUE 1 0.022 0.062 LOWER HINGE 1 0.106 0.277 UPPER HINGE 1 0.274 0.517 MAXIMUM VALUE 1 0.518 0.715 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 1.000 0.188 0.390 3.084 0.210 0.029 2 495012 1914 1977 64 1.000 0.182 0.506 3.401 0.186 0.027 3 495021 1882 1977 96 1.000 0.187 -0.045 2.670 0.219 0.019 4 495022 1886 1977 92 1.000 0.159 0.592 2.932 0.191 -0.045 5 495031 1917 1977 61 1.000 0.157 0.514 3.533 0.180 -0.001 6 495032 1922 1977 56 1.000 0.143 0.386 2.826 0.157 0.007 7 495041 1889 1977 89 1.000 0.196 0.602 3.535 0.224 -0.074 8 495042 1885 1977 93 1.000 0.211 0.409 3.063 0.243 0.003 9 495051 1868 1977 110 1.000 0.184 0.557 3.047 0.207 -0.007 10 495052 1864 1977 114 1.000 0.194 0.263 3.409 0.209 0.006 11 495081 1884 1977 94 1.000 0.195 0.947 3.929 0.210 0.050 12 495082 1868 1977 110 1.000 0.219 0.481 2.788 0.247 -0.039 13 495091 1836 1977 142 1.000 0.205 -0.044 2.820 0.247 -0.109 14 495092 1854 1977 124 1.000 0.190 0.266 3.092 0.223 -0.061 15 495101 1918 1977 60 1.000 0.235 0.493 2.712 0.276 -0.171 16 495102 1917 1977 61 1.000 0.248 0.495 3.395 0.276 -0.082 17 495111 1881 1977 97 1.000 0.202 -0.274 4.753 0.200 0.046 18 495112 1893 1977 85 1.000 0.158 -0.177 3.385 0.168 -0.029 19 495141 1831 1977 147 1.000 0.238 0.533 3.682 0.263 -0.041 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.000 0.214 -0.297 4.649 0.248 -0.047 21 495151 1900 1977 78 1.000 0.160 0.177 3.067 0.173 0.071 22 495152 1897 1977 81 1.000 0.172 0.740 5.877 0.185 -0.028 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.193 0.342 3.439 0.216 -0.022 STANDARD DEVIATION 29 0.000 0.028 0.328 0.778 0.035 0.057 MEDIAN (50TH QUANTILE) 92 1.000 0.192 0.445 3.238 0.210 -0.017 INTERQUARTILE RANGE 45 0.000 0.039 0.357 0.603 0.060 0.067 MINIMUM VALUE 56 1.000 0.143 -0.297 2.670 0.157 -0.171 LOWER HINGE (25TH QUANTILE) 65 1.000 0.172 0.177 2.932 0.186 -0.047 UPPER HINGE (75TH QUANTILE) 110 1.000 0.211 0.533 3.535 0.247 0.019 MAXIMUM VALUE 158 1.000 0.248 0.947 5.877 0.276 0.071 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.274 0.168 0.011 -0.327 2.851 -0.197 0.721 MINIMUM CORRELATION: -0.197 SERIES 495012 AND 495032 56 YEARS MAXIMUM CORRELATION: 0.721 SERIES 495101 AND 495102 60 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.426 0.197 0.275 SDEV 0.202 0.233 0.196 SERR 0.082 0.051 0.018 EPS 0.873 0.797 0.886 NSS 9.3 16.0 20.6 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1820 1977 158 0.991 0.140 0.222 3.665 0.151 -0.010 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.270 0.134 0.004 34 124 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.74 1.00 1.12 1.87 5.25 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.13 0.00 0.87 1.00 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.010 0.005 0.016 0.008 -0.014 -0.032 0.001 -0.124 0.034 -0.040 PACF -0.010 0.005 0.017 0.008 -0.014 -0.032 0.000 -0.123 0.033 -0.039 95% C.L. 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.162 0.162 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.000 0.006 0.017 0.008 -0.014 -0.032 -0.001 -0.124 0.032 -0.040 PACF 0.000 0.006 0.017 0.008 -0.014 -0.032 -0.001 -0.123 0.034 -0.040 95% C.L. 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.162 0.162 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.000 0.000 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1820 1977 158 0.991 0.158 0.109 2.777 0.125 0.465 |------------ ARSTAN CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.462 0.219 0.110 0.041 -0.015 -0.053 -0.068 -0.126 -0.049 -0.057 PACF 0.462 0.007 0.008 -0.017 -0.037 -0.039 -0.028 -0.094 0.067 -0.048 95% C.L. 0.159 0.190 0.196 0.198 0.198 0.198 0.199 0.199 0.201 0.201 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.215 0.463 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES